Question

11. The number of lightning strikes on a square kilometer of open ground in a year has a mean of 6 and a standard deviation of 2.4. These values are typical of most of the U.S. and are normally distributed. The National Lightning Detection Network uses automatic sensors to watch for lightning in a sample of 10 square kilometers.

A. What is the probability that the average number of lightning strikes in this sample area exceeds 4.4?

B. What average number of lightning strikes would represent the lowest 6.5% for the sampling distribution?

Answer 1

X has a normal distribution with mean u =6 and standard deviation o =2.4 and sample size n=10 a) probability that average number of lightning strikes in the sample area exceeds 4.4 is We have P(x>4.4) =ploration 4.4-6 2.4/10 =P(z)-2.11) =1-P(z<-2.11) =1-0.0174 =0.9826 (using z value table) 1-Normdist(X,u, o/Vn,true) =0.9825 (using excel)

POST 2.47 10) = 0.065 b) Given P(X<X)= 0.065 X-M X-6 lon z(0.065)=-1.51 X-6 =-1.51 2.4/10 x = 6-1.51*2.4/10 = 4.85 Note: Use excel values if answers are wrong